Proportional share resource management provides a flexible and useful abstraction for multiplexing time-shared resources. We present Group Ratio Round-Robin (GR3), the first proportional share scheduler that combines accurate proportional fairness scheduling behavior with O(1) scheduling overhead on both uniprocessor and multiprocessor systems. GR3 uses a novel client grouping strategy to organize clients into groups of similar processor allocations which can be more easily scheduled. Using this grouping strategy, GR3 combines the benefits of low overhead round-robin execution with a novel ratio-based scheduling algorithm. GR3 can provide fairness within a constant factor of the ideal generalized processor sharing model for client weights with a fixed upper bound and preserves its fairness properties on multiprocessor systems. We have implemented GR3 in Linux and measured its performance against other schedulers commonly used in research and practice, including the standard Linux scheduler, Weighted Fair Queueing, Virtual-Time Round-Robin, and Smoothed Round-Robin. Our experimental results demonstrate that GR3 can provide much lower scheduling overhead and much better scheduling accuracy in practice than these other approaches.